David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophia Mathematica 16 (2):182-208 (2008)
What is wrong with abstraction, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their Hale on Caesar and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and about the effects of impredicativity in abstraction principles—which underlie it; and To advance the debate of the issues thereby raised. Thanks for helpful comments to Roy Cook and to an anonymous referee. CiteULike Connotea Del.icio.us What's this?
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Citations of this work BETA
Stewart Shapiro & Geoffrey Hellman (forthcoming). Frege Meets Aristotle: Points as Abstracts. Philosophia Mathematica:nkv021.
Bob Hale (2011). The Bearable Lightness of Being (Vol 20, Pg 399, 2010). Axiomathes 21 (4):597 - 597.
Jonathan Payne (2013). Abstraction Relations Need Not Be Reflexive. Thought: A Journal of Philosophy 2 (2):137-147.
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